Linearkombinationen von iterierten Bernsteinoperatoren |
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Authors: | Günter Felbecker |
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Affiliation: | (1) Mathematisches Institut der Ruhr, Universität Bochum, Universitätsstr. 150, D-4630 Bochum, Bundesrepublik Deutschland |
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Abstract: | The Bernstein polynomials Bn(f) approximate every function f which is continuous on [0, 1] uniformly on [0, 1]. Also the derivatives of the Bernstein polynomials approach the derivatives of the function f uniformly on [0, 1], if f has continuous derivatives. In this paper we shall introduce polynomial operators, namely linear combinations of iterates of Bernstein operators, which have the same properties but, under definite conditions, approximate f more closely than the Bernstein operators. |
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